Analysis and convergence theorem of complex quadratic form as decision boundary for data classification

The application of the complex quadratic form as the decision boundary for complex-valued data classification is described. This function is always real when its matrix is Hermitian. Thus, a simple sign function to classify the input data is used. This matrix is obtained through an iterative learning process similar to the Rosenblatt algorithm. The concept of the Frobenius matrix norm is used to prove that the proposed learning algorithm converges if a solution exists. This approach is different from other complex-valued neural networks that use optimisation techniques or feature mapping. An artificial neuron that uses a complex quadratic form as the decision boundary is called a complex quadratic neural unit.